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# Chapter 24: Measures of Central Tendency Exercise – 24.3

### Question: 1

Find the median of the data:

83, 37, 70, 29, 45, 63, 41, 70, 34, 54

### Solution:

Numbers are 83, 37, 70, 29, 45, 63, 41, 70, 34, 54

Arranging the numbers in ascending order

29, 34, 37, 41, 45, 54, 63, 70, 70, 83

n = 10 (even)

### Question: 2

Find the median of the data:

133, 73, 89, 108, 94, 104, 94, 85, 100, 120

### Solution:

Numbers are 133, 73, 89, 108, 94, 104, 94, 85, 100, 120

Arranging the numbers in ascending order

73, 85, 89, 94, 94, 100, 104, 108, 120, 133

n = 10 (even)

### Question: 3

Find the median of the data:

31, 38, 27, 28, 36, 25, 35, 40

### Solution:

Numbers are 31, 38, 27, 28, 36, 25, 35, 40

Arranging the numbers in ascending order

25, 27, 28, 31, 35, 36, 38, 40

n = 8 (even)

### Question: 4

Find the median of the data:

15, 6, 16, 8, 22, 21, 9, 18, 25

### Solution:

Numbers are 15, 6, 16, 8, 22, 21, 9, 18, 25

Arranging the numbers in ascending order

6, 8, 9, 15, 16, 21, 22, 25

n = 9 (odd)

= 5th value = 16

### Question: 5

Find the median of the data:

41, 43, 127, 99, 71, 92, 71, 58, 57

### Solution:

Numbers are 41, 43, 127, 99, 71, 92, 71, 58, 57

Arranging the numbers in ascending order

41, 43, 57, 58, 71, 71, 92, 99, 127

n = 9 (odd)

= 5th value = 71

### Question: 6

Find the median of the data:

25, 34, 31, 23, 22, 26, 35, 29, 20, 32

### Solution:

Numbers are 25, 34, 31, 23, 22, 26, 35, 29, 20, 32

Arranging the numbers in ascending order

20, 22, 23, 25, 26, 29, 31, 32, 34, 35

n = 10 (even)

### Question: 7

Find the median of the data:

12, 17, 3, 14, 5, 8, 7, 15

### Solution:

Numbers are 12, 17, 3, 14, 5, 8, 7, 15

Arranging the numbers in ascending order

3, 5, 7, 8, 12, 14, 15, 17

n = 8 (even)

### Question: 8

Find the median of the data:

92, 35, 67, 85, 72, 81, 56, 51, 42, 69

### Solution:

Numbers are 92, 35, 67, 85, 72, 81, 56, 51, 42, 69

Arranging the numbers in ascending order

35, 42, 51, 56, 67, 69, 72, 81, 85, 92

n = 10(even)

### Question: 9

Numbers 50, 42, 35, 2x + 10, 2x – 8, 12, 11, 8 are written in descending order and their median is 25, find x.

### Solution:

Given the number of observation, n = 8

= 2x + 1

Given Median = 25

∴ 2x + 1 = 25

⇒ 2x = 24

⇒ x = 12

### Question: 10

Find the median of the following observations: 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?

### Solution:

Given the numbers are  46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33

Arranging the numbers in ascending order

33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92

n = 11 (odd)

= 6th value = 58

If 92 is replaced by 99 and 41 by 43

Then the new values are: 33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99

n = 11 (odd)

= 6th value = 58

### Question: 11

Find the median of the following data: 41, 43, 127, 99, 61, 92, 71, 58, 57. If 58 is replaced by 85, what will be the new median?

### Solution:

Given the numbers are 41, 43, 127, 99, 61, 92, 71, 58, 57

Arranging the numbers in ascending order

41, 43, 57, 58, 61, 71, 92, 99, 127

n = 9 (odd)

If 58 is replaced by 85

Then the new values be in order are:  41, 43, 57, 61, 71, 85, 92, 99, 127

= 5th value = 71

### Question: 12

The weights (in kg) of 15 students are: 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median.

### Solution:

Given the numbers are 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30

Arranging the numbers in ascending order

27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 44, 45.

n = 15 (odd)

= 8th value = 35 kg

If the weight 44 kg is replaced by 46 kg and 27 kg is replaced by 25 kg

Then the new values be in order are: 25, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 45, 46

= 8th value = 35 kg

### Question: 13

The following observation s have been arranged in ascending order. If the median of the data is 63, find the value of x: 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95.

### Solution:

Total number of observation in the given data is 10 (even number). So median of this data will be mean of 10/2 i. e, 5th observation and 10/2 + 1 i. e, 6th observation. So,

⇒ 63 = x + 1

⇒ x = 62